A cylinder with a mass M and radius r is floating in a pool of liquid. The cylinder is weighted on one end so that the axis of t
he cylinder stands vertically. The total length of the cylinder is L. The density of the fluid is rho.
a. When the cylinder is in equilibrium, a portion of it is submerged in the liquid. What is the vertical length h of this submerged portion? Your answer should use only the given symbols M, r, L, and rho as necessary, as well as the constant g.
b. The cylinder is now displaced a distance y from the equilibrium position, such that |y| < h, and released from rest. Let the +y-axis be upward, so that if the cylinder is pulled up, y is positive, but if it is pushed down, y is negative. Immediately after it is released, what is the y-component of the acceleration ay of the cylinder? Your answer should use only the given symbols M, r, L, y, and rho as necessary, as well as the constant g.
c. The result of part (b) implies the cylinder is now in simple harmonic motion. What is the period T of the cylinder's oscillations
